In a so-called fast idle system, the amount of intake air introduced into the engine during the idling condition of the engine is controlled in accordance with the temperature of the engine, so that excess air is introduced into the engine when it is cold. As a result of the supply of excess air, the idling speed of the engine at low temperature is maintained to a high speed value N.sub.F. When the engine is under deceleration the throttle valve is also under idling position. During deceleration condition, the supply of fuel is stopped in order to prevent the over heating of the exhaust system by detecting a predetermined rotational speed value N.sub.cut. If the rotational speed of the engine is dropped to a predetermined value N.sub.RTN lower than the first predetermined value N.sub.cut the fuel is supplied.
When the fast idling operation is carried out, the idling rotational speed is high and can exceed the predetermined value N.sub.cut. At this situation the fuel supply is stopped during the idling condition, causing an unstable idling operation to take place. In order to prevent this situation from occurring, in a conventional technic, values of N.sub.cut are, in accordance with the temperature of the engine, stored in the memory, each of the value N.sub.cut is higher than the values of N.sub.F at any temperature of the engine. In this case, the value of N.sub.cut is always larger than the value of N.sub.F, so that unstable idling is prevented. However, this conventional system suffers from a drawback in that the computer must have a large number of memory cells.